Is there any way to recover/rebuild the logs or any other procedure to make it work again? We do not have backups.
That depends on how you define "work again" as the log holds information to make the database consistent. This means even if you did get the database back up and running there is no guarantee that the data in it is correct. So maybe that "works" for you but if it's something like accounts payable, that might not be a solution.
You can give this a shot for user databases, but again YMMV and the data shouldn't be trusted. If there is a way to re-create the database and import the data, that would be best.
With system databases the easiest method is to rebuild them from the media. Since
master is an issue in this instance, you'll lose information such as logins (if they are SQL logins their associated passwords), linked servers, any instance wide certificates, etc.
If you get this back up and running, I'd implement backups and lock down servers and permissions.